A Graph Symmetrisation Bound on Channel Information Leakage under Blowfish Privacy

TL;DR

This paper establishes a bound on information leakage for Blowfish privacy mechanisms by leveraging graph symmetry, extending privacy-utility guarantees to more flexible privacy policies.

Contribution

It introduces a novel graph symmetrisation approach to bound min-entropy leakage in Blowfish privacy, generalizing existing differential privacy results.

Findings

Bound on min-entropy leakage for Blowfish privacy mechanisms.

Construction demonstrating the tightness of the bound.

Extension of symmetry-based leakage analysis to arbitrary privacy policies.

Abstract

Blowfish privacy is a recent generalisation of differential privacy that enables improved utility while maintaining privacy policies with semantic guarantees, a factor that has driven the popularity of differential privacy in computer science. This paper relates Blowfish privacy to an important measure of privacy loss of information channels from the communications theory community: min-entropy leakage. Symmetry in an input data neighbouring relation is central to known connections between differential privacy and min-entropy leakage. But while differential privacy exhibits strong symmetry, Blowfish neighbouring relations correspond to arbitrary simple graphs owing to the framework's flexible privacy policies. To bound the min-entropy leakage of Blowfish-private mechanisms we organise our analysis over symmetrical partitions corresponding to orbits of graph automorphism groups. A construction meeting our bound with asymptotic equality demonstrates tightness.